Electrical differentiator



Dec. 10, 1946.

H. G. ocH ETAL 2,412,227

ELECTRICAL DIFFERENTIATOR Filed May 1, 1941 FIG. I

i ii a H. 6.0CH WVENTORS' KOSWARTZEL JR.

A TIORNE Patented Dec. 10, 1946 UNITED STATES PATENT OFFICE ELECTRICAL DIFFERENTIATOR Henry G. Och, West Englewood, and Karl D. Swartzel, Jr., Teaneck, N. J., assig-nors to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application May 1, 1941, Serial No. 391,332

3 Claims. (Cl. 17844) 1 2 This invention relates to electrical measuring circuit of the vacuum tube 4 assist in maintaincircuits and particularly to an electrical network ing the proper phase relationships in the amplifor deriving a function of the input voltage. fier so that the output voltage of the amplifier The object of the invention is an electrical netwill accurately represent the desired value.

work for continuously deriving the differential or 5 In the following equations let time derivative of the input voltage. =t voltage to be analyzed,

A feature of the invention is the use of a reverse feedback circuit associated with a linear RIZthe resistance of resistor amplifier in such manner as to produce in the Rzzthe resistance f resistor n output of the amplifier a voltage varying as the in Rzthe resistance resistor '3 or e=the output voltage,

differential of the input voltage. czthe capacitance f capacitor In many measuring devices such artillery S=the change of the plate current of vacuum predictors, airplane bomb sights, vibration meastube a due to a unit voltage applied to the grid uring devices and many others, it is necessary to of vacuum tube 2, that is the over-mu trans obtain the rate of change of some measurable i5 conductance of the complete ampufien quantity. In accordance with the present invention this measurable quantity is expressed as a Using the Prmclples Set forth m Efatent variable electrical voltage which is applied to the 2,102,571, December 21, 1937, Black It can input of an electrical network. The network r be shown that modifies the applied voltage to produce in the 3 RC #5 1 output circuit a voltage varying in accordance (f with the rate of change or differential of the in- 23120 +3 put voltage, and, in some cases, a voltage vary- (1) i g gz w i P Input voltage Where o is the gain around the feedback loop Fig. 1 diagrammatically shows an electrical and is equal to network embodying one aspect of the invention;

- S X Fig. 2 shows the network of Fig. 1 modified to R R2 122 R| 122 R1 produce a pure dlfrerentlal voltage- When the gain around the feedback loop is large, The voltage to be analyzed is cmwmwnally say 1000, the last two members of the gain equadesignated by the voltage source 60, and is applied on are Very nearly unity and the gain can be to the input of the network through a resistor I. expressed as This voltage is applied directly to thecontrol cleatrode, or grid of the first vacuum tube 2, which J may have a conventional grid biasing resistor 3 e R\ 1+ 2 p R1 80 {E R1 pm (3) in the cathode circuit. The vacuum tube 2 is But 10 is the common mathematical operator 1 coupled to the vacuum ube by the known nelidioatlng differentiation with respect to time and, Wor Comp is t e resistors 5 6 and The therefore, the output voltage e includes a comvacuum tube 4 is similarly coupled to the vacuum 4 [30119111] r rtional t e and a component proube 3 y ans o e known network portional to the time derivative or differential prising the resistors 9, l0 and H. The output of of the vacuum tube 8 is supplied to the load resistor By a it bl hoic of the circuit elements l2 and is available as a voltage appearing across R R and c, and providing the gain around the this resistor. Power is fed back from the anode f edback loop is l it; i vid t from Equation of e Vacuum t e 3 t0 e Control electrode, 3 that the absolute, as well as the relative, values grid of the vacuum tube 2 through the serially of t signal compgnent,

connected resistors l3 and I4. A capacitor [5 is connected from the junction of the resistors I3 and I4 to ground, that is, eifectively to the cath- 0 R1 ode circuits of the vacuum tubes. and the differential component The capacitors l6 and I9, respectively in serial R20 relationship with the resistors l1 and 20 in shunt )pe to the input circuits of the vacuum tubes 4 and 8, and the capacitor It! in shunt to the output may be controlled within a certain range, but,

as a practical matter, the signal component cannot be made equal to zero, so as to give a pure differential component. However, this result may be obtained, as shown in Fig. 2, by canceling out the signal component.

In Fig. 2, the amplifier 2| represents the linear amplifier of Fig. 1, and circuit elements having reference characters similar to those in Fig. l have similar functions. The output of the network 2| is supplied through a resistor 23, to a summing amplifier 22, of the type disclosed in U. S. application Serial No. 391,331, to K. D. Swartzel, Jr., filed of even date herewith. The summing amplifier 22 has a feedback path through the impedance 25, and will produce in its output circuit a voltage proportional to the algebraic sum of the voltages supplied to the input circuit. Signal voltage from the source 60 is supplied directly through the resistor 24 to the input of the summing amplifier 22. As the network 2| includes an odd number of vacuum tubes in cascade, the signal voltage supplied by the network 2| to the summing amplifier 22 is reversed in phase with respect to the signal voltage supplied through the resistor 24.

Let

Ri=resistance of resistor l, R1a=resistance of resistor 13, Ru=resistance of resistor 14. R23=resistance of resistor 23, Rz4=resistance of resistor 24.

Then if lz-l' 14 fli R1 R24 the signal voltages supplied to the input of the summing amplifier 22 will just cancel each other, and the output of the summing amplifier 22 will contain only the diiferential component.

It will generally be found that the capacitor l has a certain amount of leakage resistance, which may be considered as a resistor of suitable value in shunt with the capacitor l5, which will tend to produce a component of signal voltage in the output of the amplifier 2|, and thus change the relative values of signal voltage and differential voltage in the output, compared to the values given by a perfect capacitor. By suitable choice of the values of the resistors R1, R13, R14. R23. R24, R25, and the capacitor C15, the relative values of signal voltage and differential voltage may be made to approximate the values obtained with a perfect capacitor.

By connecting a number of the circuits shown in Fig, 2 in tandem, it is obvious that the second. or higher, differentials of the signal voltage may be obtained.

In a typical embodiment of the invention, the resistor l was 4 megohms, the resistor 3 was 1500 ohms, the resistors 5, 6, I, 9, II), II were respectively A, 2, 1% and 1 megohms, the resistor l2 was 6000 ohms, the resistors l3 and M were each 2 megohms, and the resistors i1 and 20 were each 100,000 ohms. The capacitors I5, IE, I8, l9 were respectively 1, .001, .0001, .03 microfarads. The vacuum tubes 2, 4, 8 were commercial vacuum tubes respectively designated by the trade-names 6SC7, 6SJ7 and 6Y6G. A TOO-volt battery, grounded at the mid-point, was used, +350 volts being applied to the anodes of tubes 2 and 4, +250 volts to the anode of tube 8, volts to the screen grid of tube 5, ground or zero volts to the cathode of tube 4 and the screen grid of tube 8, volts to the cathode of tube 8 and 350 volts to the grid of tube 4.

What is claimed is:

1. In combination, a source of voltage to be analyzed, a linear amplifier having an input and an output circuit, a first resistor in serial relationship with said source connected to the input circuit of said amplifier, and a feedback path from said output circuit to said input circuit includ ing two resistors connected in serial relationship in said path, and a capacitor connected from the junction of said resistors in shunt to said path, whereby the output of said amplifier contains components corresponding to the voltage from said source. and to the differential or time derivative of said voltage, a second linear amplifier having an input and an output circuit, a fourth resistor in serial relationship with the output circult of said first amplifier and the input circuit of said second amplifier, a feedback path from the output circuit to the input circuit of said second amplifier, and a fifth resistor in serial relationship with said source connected to the input circuit of said second amplifier.

2. The combination in claim 1 in which the ratio of the sum of said two resistors to said first resistor equals the ratio of said fourth resistor to said fifth resistor.

3. The method of producing a voltage varyin; with the rate of change of a signal voltage, which comprises amplifying said signal voltage, feeding back a portion of said amplified voltage of such magnitude and phase as to produce a component of voltage varying with the rate of change of said signal voltage, supplying said amplified signal voltage and said component to a utilization cir cuit, and supplying to said utilization circuit signal voltages of reversed phase to neutralize the amplified signal voltage in said utilization circuit.

HENRY G. OCH. KARL D. SWARTZEL, JR. 

